What is (\partial)/(\partial x)(1/(x+1)) ?

The answer to (\partial)/(\partial x)(1/(x+1)) is -1/((x+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(1/(x+1))

\frac{\partial}{\partial x} (\frac{1}{x + 1})

- \frac{1}{( x + 1 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x + 1})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial x} ((x + 1)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 1 ) ^{2}} \frac{\partial}{\partial x} (x + 1)

= - \frac{1}{( x + 1 ) ^{2}} \frac{\partial}{\partial x} (x + 1)

\frac{\partial}{\partial x} (x + 1) = 1

= - \frac{1}{( x + 1 ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( x + 1 ) ^{2}}

\int (2 t^{2} - 1)^{2} d t

2 (x) + 1

- 7 x^{2} + 63, - x^{2} + 9

x \to - 1 lim (\frac{1 - x ^{2}}{x + 1})

\int (4 x^{3} - 1)^{2} d x

What is (\partial)/(\partial x)(1/(x+1)) ?
The answer to (\partial)/(\partial x)(1/(x+1)) is -1/((x+1)^2)